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Blackjack (Encrypted Version)
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Introduction
This section discusses the encrypted format of blackjack, typically found in cryptocurrency-based casinos, presuming the reader has a grasp of traditional blackjack rules. blackjack .
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Analysis
In the case of playing at Crypto.Games, the unusual rules are as follows:
- 4 decks
- Shuffle after each hand
- Dealer does not peek for blackjack
- Blackjack pays 6:5
- Dealer hits on Soft 17
- Double on any two cards
- Hit split aces
- Early surrender
- A combination of a ten and ace after a split counts as a blackjack.
- Double after split allowed
- Player may split once only (I assume)
Without factoring in early surrender or the 10-A rule after splitting counting as blackjack, my analysis indicates a house edge of 1.91% using basic strategy. Still, my findings suggest that the impact of the two rules not accounted for by the calculator is 0.74%. Hence, the overall house edge stands at 1.17%, which is relatively steep for an online blackjack game. blackjack house edge calculator This is how Crypto.Games randomly selects cards from a four-deck shoe for their blackjack version. blackjack rule variations The SHA-256 hash of the Server Seed is revealed to the player prior to making a bet.
Fair Gaming
Once the bet is placed, the Server Seed and Client Seed are combined, in that sequence.
- Next, a SHA-512 hash is generated from the combined seeds as outlined in the previous step.
- Take the first two characters from the hash generated in the previous step, starting from the left side.
- Convert these two characters from hexadecimal to decimal values. If you're unfamiliar with this process, I've detailed base-16 math on my Dice (Encrypted Version) page.
- If the resulting decimal value from the previous step is 207 or lower, that number corresponds to a specific card in the 208-card shoe.
- If that card number has not yet appeared in the hand, map it to an actual card. Here’s how to determine that:
- To ascertain the rank, divide the card number by 13 and take the remainder. Map that remainder to ranks as follows: 0 to ace, 1 to 2, 2 to 3, up to 12 for king.
- To establish the suit, divide the card number by 13 and ignore the remainder. Then, take that quotient, divide by 4, and take the remainder, mapping it to suits as follows: 0 to spades, 1 to hearts, 2 to diamonds, 3 to clubs.
- If, however, the output from the fifth step exceeded 207, or if that specific card was already found, disregard those two hash digits.
- Move two positions forward in the hash and revert to step three, continuing this until reaching the end of the hash, ensuring a supply of cards beyond what is needed for a single blackjack hand.
- Here’s an example of how this process unfolds for a specific hand.
- The image from the Fair Gaming panel was captured before a bet was placed. Ensuring a fair game involves entering and logging a new Client Seed (a string of random characters suffices) and the hash for the next Server Seed, referred to as 'Next server seed SHA256.' Here are these items:
Example
I often find it handy to copy and paste this information into Notepad when navigating this process.
In the image, I initiated a bet of 0.00001 BTC (equivalent to around 10 cents). The player uses this bet to acquire ten chips, subsequently betting all ten. I’m not clear on why this adds complexity.
Client seed =5v5b85n85vb856nvbn5vbn
- Next server seed SHA256 =
581b31f8cd6e5d4bb510ac0e53a440af7baab92f8f1f220eff14e20201e0b1f6
My opening hand totalled 11 against a dealer's three, prompting me to double; I ended up drawing a 3. The dealer had a hidden 5, making a total of 8, then drew a king, yielding 18. As a result, I lost with a score of 14 to 18.
Next, I return to the Fair Gaming panel to verify the fairness of the game, which is illustrated by the predetermined card order prior to my bet. By following the outlined steps:
According to the Fair Gaming panel, the Server Seed was
Yt5IDwsb3Ldc5vyusvcQNfLqqjoYmCHGRkasqXNQ
- We compare the hash result from step two with the 'Next server seed SHA256' recorded before the bet to confirm they align. If there’s a mismatch, it suggests an error on your part or potential dishonest behavior from the casino. Here they match, affirming the predetermined card order.
To confirm the cards you received, combine the Server Seed and Client Seed, following the order specified. This will produce. - We take the SHA-256 Hash of that to get581b31f8cd6e5d4bb510ac0e53a440af7baab92f8f1f220eff14e20201e0b1f6.
- Yt5IDwsb3Ldc5vyusvcQNfLqqjoYmCHGRkasqXNQ5v5b85n85vb856nvbn.
- If you've chosen to include a nonce, it will be at the end of your Client Seed.Now, compute the SHA-512 hash of the combined hash derived from step four. The rationale behind employing two different hashing algorithms (SHA-256 and SHA-512) remains unclear. The resulting hash will be 2b87fbc5eac7368ef393c8ab292f71a0251702f6db028ca8a855bfaa541b78df3ae996ad22ac022588a46231ed32180d5cbde86dff5d2368cbb7658332bbb9bc.Extract the first two characters, which are 2b , and convert them into decimal: 2b = 2*16 + 11 = 43.
- As 43 <= 207, this value is then translated into a card: rank = mod(43,13) = 4, which corresponds to a 5. For the suit = mod(int(43/13),4) = mod(3,4) = 3, this leads to clubs. Hence, the first card drawn is the 5 of clubs.
- Moving two positions ahead in the hash from step four brings us to 87 . Converting this from hexadecimal to decimal gives us: 8*16 + 7 = 135.
- Since this value of 135 <= 207 and has not previously appeared, we convert it into a card: rank = mod(135,13) = 5, leading to a 6. The suit = mod(int(135/13),4) = mod(10,4) = 2, which corresponds to diamonds. Thus, the second card revealed to the player is the 6 of diamonds.
- Advancing two positions in the hash from step four gives fb . When converting this from hexadecimal to decimal: 15*16 + 11 = 251.
- Moving ahead two more positions in the hash results in c5 . The conversion from hexadecimal to decimal yields: 12*16 + 5 = 197.
- Since 197 <= 207 and hasn’t been previously drawn, this converts into a card: rank = mod(197,13) = 2, leading to 3. For the suit = mod(int(197/13),4) = mod(15,4) = 3, which maps to clubs. Therefore, the first face-up card dealt to the dealer is the 3 of clubs.
- Since 251 > 207, we skip those two positions.
- Advancing two positions in the hash from step four reveals ea . The conversion from hexadecimal to decimal makes: 14*16 + 10 = 234.
- Proceeding two more positions in the hash gives c7 . The conversion from hexadecimal to decimal results in: 12*16 + 7 = 199.
- Since 199 <= 207 and hasn't been encountered yet, this converts into a card: rank = mod(199,13) = 4, yielding a 5. The suit = mod(int(199/13),4) = mod(15,4) = 3, matching to clubs. Thus, the second face-down card dealt to the dealer becomes the 5 of clubs.
- Since 234 > 207, we skip those two positions.
- Advancing two positions in the hash from step four leads to 36 . The conversion from hexadecimal to decimal results in: 3*16 + 6 = 54.
- Wizard of Odds presents an encrypted variant of blackjack.
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- 1: Expected return table based on total dependence for an endless deck.
- 2a: Chances of dealer getting blackjack after checking their cards.
- The player loses 14 to 18.
- 2b: Odds of dealer getting blackjack prior to checking their cards.
3a: Noteworthy exceptions for single-deck basic strategy in S17.
- Go to the PHP Sandbox .
- Enter the Server Seed on line 3.
- Enter the Client Seed on line 4.
- 3b: Noteworthy exceptions for double-deck basic strategy in S17.
- Click \"Execute Code.\"
3c: Noteworthy exceptions for single-deck basic strategy in H17.
4: Insights into the standard deviation of blackjack.
5: Expected returns based on infinite deck according to player hand and dealer's visible card.
9: Expected returns based on card composition for one to eight decks.
$client_seed = \"5v5b85n85vb856nvbn5vbn\";
10: Comparing continuous shuffling devices with cut cards.
$rank_array=array(\"A\",2,3,4,5,6,7,8,9,10,\"J\",\"Q\",\"K\");
13: Probabilities associated with the first four cards dealt.
$cards_found=0;
$position=0;
15: Comparing house edge using total-dependent strategy against composition-dependent strategy.
16: Basic strategy applied when both dealer cards are visible.
18: Exceptions in basic strategy when dealing with three to six cards.
19: Splitting strategy in blackjack when a back-player places a bet.
do
{
20: Doubling strategy in blackjack when players can double after splitting aces.
$hex_to_dec=hexdec($first_two);
if ($hex_to_dec <=207)
{
$repeat=0;
if ($cards_found>0)
{
for ($i=0; $i<$cards_found; $i++)
{
if ( $hex_to_dec == $card_array[$i])
{ $repeat=1; }
}
}
if ($repeat==0)
{
21: An overview of the straightforward strategy provided by the Wizard.
$cards_found++;
$rank=$hex_to_dec;
$suit=intdiv($hex_to_dec,13)%4;
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}
}
$position+=2;
if ($position==128)
{
This section informs about the encrypted version of blackjack, typically found in cryptocurrency-based casinos. It assumes prior knowledge of standard rules.
$cards_found=10;
}
}
while ($cards_found<20);
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if ($server_seed_hash==$next_hash)
{ echo \"Server Seed match.
\"; }
else
{
echo \"SERVER SEED MISMATCH!
\";
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}
// Procedure
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For the game offered at Crypto.Games, the unique set of rules includes the following:
If a player splits and then draws a ten and an ace, it counts as blackjack.
Without taking into account rules like early surrender and the aforementioned situation with blackjack after splitting, my calculations suggest a house edge of 1.91% using basic strategy. However, my analysis indicates the unaccounted rules in the calculator add up to 0.74%. This results in an overall house edge of 1.17%, which is relatively high for an online blackjack experience.
The following outlines the methodology used by Crypto.Games in selecting cards randomly from a four-deck shoe for their blackjack game.
The SHA-256 hash of the Server Seed is disclosed to the player before wagers are placed.
Once the bet is placed, the Server Seed and Client Seed are combined in that specific order.
The SHA-512 hash is then computed from the combination derived in the previous step.
Two characters from the hash produced in the previous step are selected, starting from the left.
The two characters obtained in the previous step are converted from hexadecimal to decimal. If this conversion is unfamiliar, a discussion of base-16 mathematics can be found on my Dice (Encrypted Version) page.
If the resulting value from the previous step is 207 or lower, it corresponds to a specific card in the 208-card shoe.
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